Lenses formed by arrays of reflectors

ABSTRACT

A lens, suitable for directing radiation, comprises an array of planar reflecting elements or slats. Each reflecting element is of non-uniform extent or surface area t and/or is of non-uniformly spacing d from adjacent elements. The elements may be parallel or non-parallel. Each element is positioned such that the ratio of spacing d n  to extent t n  is determined by the angle of incidence on the nth element γ n  as is given by the relationship (a) where d n  is the spacing between the nth and (n+1)th adjacent elements of the lens, t n  is the length of the nth element and M is the magnification of the lens.

TECHNICAL FIELD

This invention concerns optical elements for use as lenses, collimatorsand collectors of radiation. More particularly, it concerns lensesformed by arrays of reflecting slats, which are suitable for focusing,collimating, or collecting radiation.

BACKGROUND TO THE INVENTION

The specification of International patent application No PCT/AU93/00453discloses a range of radiation control devices (including radiationdeflectors, concentrators and lenses), each of which is formed by anarray of substantially identical reflecting elements. In addition, it isnoted in the specification of International patent application NoPCT/AU93/00453 that an array of elongate reflectors can be used forone-dimensional focusing (line focusing) of radiation, and that two sucharrays of reflectors, crossed at right angles, will form the equivalentof an array of reflecting channels, with each channel having arectangular cross-section (which is a square cross-section when thereflectors of each array of parallel reflectors have the same spacing).Thus a two-dimensional focusing array or lens can be constructed usingtwo arrays of reflector strips or slats.

One advantage possessed by optical devices formed by an array ofreflecting slats--including the "90° crossed-slats" lens referred toabove--is that the surfaces of the elongate reflectors can be polishedand examined for flaws before the arrays of reflectors are assembled toform the optical device. This feature, as also noted in thespecification of International patent application No PCT/AU93/00453,permits the reflective surfaces of the slats to be coated in a mannerwhich ensures that those surfaces are selectively reflective atpredetermined wavelengths.

The present inventor has also shown that this type of 90° crossed-slatslens has an additional advantage over the devices previously used tofocus x-radiation (and other radiation having a wave-like character)onto a focal zone. The additional advantage is a significant increase inthe "intensity gain" of the lens or focusing device. In this field, thegain, G. of a lens or focusing device is defined by the relationship:##EQU1## where I_(d) is the intensity of radiation in the focal spot orzone of the device and I_(o) is the intensity of radiation at the samelocation in the absence of the focusing device.

DISCLOSURE OF THE PRESENT INVENTION

In further developmental work with slatted lenses and crossed-slatslenses, the present inventor has ascertained that improved slattedlenses with a focussing efficiency approaching 100% can be produced ifthe individual reflectors or slats of the lens are not essentially thesame as each other, but the slats have a progressive change in surfacearea as the distance of the slats from the axis of the lens increases.The lenses are preferably produced such that, (i) the slats are planar,and (ii) the change in surface area of the slats with distance from theaxis of the lens will be a decrease in surface area. However, in themanufacture of such lenses, the slats of a lens may conveniently be ingroups of equal "front-to-back" length, t, but with varying spacing, d,between the slats in a group, such that the ratio of d_(n) /t_(n) isdetermined by the angle of incidence, on the nth slat of the lens, ofradiation from a point source on the lens axis, γ_(n), as isapproximately given by the relationship: ##EQU2## for a magnification ofone, and, perhaps more precisely given by: ##EQU3## where d_(n) is theseparation (or spacing) between the nth and (n+1)th slats of the lens,t_(n) is the extent of the nth slat in a direction parallel to the lensaxis, and, M is the magnification of the lens.

Preferably, the separation of the slats of the lens (that is, thespacing--or average spacing--between adjacent slats of the lens) will besuch that no slat or reflector creates a "shadow" on its adjacent outerreflector in the lens, from radiation from a point source at an expectedpoint on the axis of the lens. This usually means that the spacing, d,between adjacent slats will increase progressively with the distance ofthe slat from the axis of the lens, and the possibility of multiplereflections of radiant energy from that source, in the space betweenadjacent slats, will be minimised. In the case of a focusing lens, thiswill maximise the energy focused by the lens, which will furtherincrease the gain of the lens.

Thus, according to the present invention, there is provided an improvedslatted lens which comprises a plurality of spaced-apart slats disposedsymmetrically about the axis of the lens, each slat having one facewhich is towards the axis of the lens, said one face having a reflectivesurface, characterised in that the relationship between (i) the length,t, of a slat (ii) the spacing, d, between adjacent slats, and (iii) theangle of incidence, γ, of radiation from a point source on the axis ofthe lens, for the nth slat from the lens axis, is given by ##EQU4##

Although this definition of the new slatted lens of the presentinvention requires only one face of each slat to have a reflectivesurface, in many instances (for example, if the lens is to be used withan extended source of radiation, or for concentrating partially diffusedradiation) it will be preferable for both faces of each slat to have areflective surface.

The generatrix (i.e. a line normal to each of the reflectors) of a lenswith plane reflectors (slats) may have (i) a parabolic shape when thelens is to be used to focus a parallel beam, or to produce a collimatedbeam from a point source, (ii) an elliptical shape to focus a convergingbeam, or to produce a diverging beam from a point source, or (iii) ahyperbolic shape to focus a diverging beam, particularly a convexhyperbolic shape to achieve a higher intensity gain in the focal spot(demagnification), or a concave hyperbolic shape for magnification. Innarrow angle lenses the generatrix will typically have the shape of partof a circular cylinder, as a parabola, a hyperbola or an ellipse allapproximate to a circle for small off-axis angles.

If the envelope of the leading edges or the trailing edges of the slatsof the slatted lens is substantially a plane which is orthogonal to theaxis of the lens, two such slatted lenses may be placed with theirsubstantially planar slat edges closely adjacent to each other(preferably abutting each other) and with their slats "crossed at 90°",to form an improved crossed-slats lens wherein the two one-dimensionallenses have a common centre of curvature. As will be understood topersons skilled in the art, a lens of this type is described above andin the specification of International patent application NoPCT/AU93/00453, the details of such specification of which should beconsidered to be entirely incorporated herein by the reference thereto.

In one broad form, the present invention provides a lens, suitable fordirecting radiation, comprising an array of planar reflecting elements,characterised in that each of said elements are of non-uniform extent orsurface area and/or are non-uniformly spaced from adjacent elements.

Preferably, the surface area of each element decreases relative toadjacent elements, as the distance of each element from an axis of saidlens increases.

Alternatively, but also preferably the spacing between each elementincreases as the distance of each element from an axis of said lensincreases, whilst the extent of each element remains the same.

In a preferred form, each element is spaced and/or has a surface areasuch that no element creates a shadow on an adjacent element positionedoutwardly thereof.

Preferably, the ratio of d_(n) /t_(n) is determined by angle ofincidence γ_(n) of radiation on each element of said lens as is given bythe relationship: ##EQU5## where d_(n) is the spacing between the nthand (n+1)th adjacent elements of the lens, and t_(n) is the length ofthe nth element.

Most preferably, the ratio of d_(n) /t_(n) is determined by the angle ofincidence γ_(n) of radiation on each element of said lens as is given bythe relationship: ##EQU6## where d_(n) is the spacing between the nthand (n+1)th adjacent elements of the lens, t_(n) is the length of thenth element, and M is the magnification of the lens.

In a preferred form, either one or both faces of the element is providedwith a reflective surface.

Preferably, the generatrix of the lens is of simple or compound,hyperbolic (concave hyperbolic or convex hyperbolic), parabolic,elliptic or circular shape.

In a preferred form a cross-slatted lens is formed of two lenses ashereinbefore described, wherein their respective elements are placedwith their substantially planar edges closely adjacent to each other(preferably abutting each other) and with their elements `crossed at90°`, the two lenses having a common centre of curvature.

Most preferably, the cross-slatted lens forms an improved cross-slattedlens as disclosed in the specification of PCT/AU93/00453.

Preferably, said reflective elements are formed as planar slots intransparent material and whereby reflection is due to total internalreflection.

In an alternatively preferred form, said reflective elements arecrystals or multi-layer mirrors and reflection is due to Braggreflection.

In another preferred form, a multi-lens is formed of two lenses ashereinbefore described wherein said multi-lens is used as a beam profilehomogeniser to arrange a first type of beam into a second type of beam.

In a preferred embodiment, said lens is utilised as a sky-lightenhancer.

In another preferred embodiment, said lens is utilised as a solarconcentrator, in the form of a simple or compound hyperbolic shape.

These and other features of the present invention will be betterunderstood from the following description of embodiments of the presentinvention, which are provided by way of example only. In the followingdescription, reference will be made to the accompanying drawings.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS

FIG. 1 is schematic sectional representation of a slatted lens havingplanar reflectors and having a magnification of 1, constructed inaccordance with the present invention;

FIG. 2 is a schematic representation of a modified form of the lens ofFIG. 1;

FIG. 3 is a representation, similar to that of FIG. 1, of anothermodified form of the slatted lens shown in FIG. 1, having amagnification which is greater than 1 or less than 1 (depending on theway in which the lens is used);

FIG. 4(a) is a representation, similar to that of FIG. 3, of anothermodified form of the lens to focus parallel beams, in which thegeneratrix (i.e. a line normal to each of the reflectors) of a lens withplane reflectors (as in FIG. 3) is a parabola;

FIG. 4(b) is a representation of another modified form of the lens tofocus converging beams, in which the generatrix of the lens with planereflectors is of elliptical shape;

FIG. 4(c) is a representation, of another modified form of the lens tofocus diverging beams, in which the generatrix of the lens with a planereflectors is a hyperbola;

FIG. 4(d) is a representation of another modified form of the lens formagnification, in which the generatrix of the lens with plane reflectorsis of concave hyperbolic shape;

FIG. 5 illustrates a lens similar to that in FIG. 3, but with thereflectors formed as planar slats in a transparent material withrefractive index greater than 1, and reflection is due to total internalreflection;

FIG. 6 illustrates a lens to focus X-rays similar to that in FIG. 3, butwherein the reflectors are crystals or multi-layer mirrors, andreflection is due to Bragg reflection;

FIG. 7 illustrates an improved 90° crossed-slats lens formed by twoone-dimensional slatted lenses of the types featured in FIGS. 1 to 3crossed at right angles, various views being shown in FIGS. 7(a) to7(d);

FIG. 8 illustrates an example of an array designed as a beam profilehomogeniser to arrange a Gaussian beam into a `top hat` beam;

FIG. 9 illustrates a practical application of a lens constructed inaccordance with the present invention, embodied as a 2-D sky lightenhancer made of blocks of transparent plastics material with slots orreflectors for total internal reflections, FIG. 9(a) showing anelevational cross-sectional view thereof, and FIG. 9(b) showing a topview thereof;

FIG. 10 illustrates an elevational cross-sectional view of a trough-likesolar concentrator formed by an array of reflectors which may be formedof parabolic, hyperbolic and/or elliptical shape; and

FIG. 11 illustrates, in FIGS. 11(a) and 11(b) an elevationalcross-sectional views of compound hyperbolic concentrators.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

FIG. 1 is a sectional view of a slatted lens 10 having a plurality ofplanar slats 12 mounted symmetrically above and below the axis 11 of thelens. The face of each slat 12 which is towards the axis 11 has areflective surface. The other face of each slat 12 may also have areflective surface. Normally, each slat 12 will extend the same distancein the plane orthogonal to the drawing, as each other slat in the array.A point source 13 of radiation is positioned on the axis of the lens 10.As shown by a series of ray paths, the lens 10 acts to focus radiationfrom the source 13 onto a focal zone 14, which will be an elongate orline focal zone, extending in a direction orthogonal to the plane ofFIG. 1.

For the sake of clarity, FIG. 1 shows only five reflectors or slats oneach side of the lens axis 11. In practice, many more reflective slatswill normally be used to produce a slatted lens, particularly if thesource 13 is a source of x-rays. A similar comment applies to theillustrated lenses in the other Figures of the accompanying drawings.

It will be noted that in the lens featured in FIG. 1, the slats 12 whichare closest to the lens axis 11 have a greater surface area than theslats 12 which are remote from the lens axis 11, and that there is aprogressive change in the surface area of the slats with the distance ofa slat from the lens axis 11. In addition, the spacing between the slats12 which are remote from the lens axis 11 is greater than the separationof the slats which are adjacent to the lens axis. These dimensionalchanges are chosen to ensure that (i) all radiation from the source 13which is incident on the lens 10 is reflected towards the focal zone 14by a reflective surface of a slat 12 of the lens, and (ii) no radiationfrom the source 13 is reflected more than once in its passage through achannel between two adjacent slats of the lens. Thus essentially allradiation from the source 13 which is incident upon the slatted lens 10is directed to the focal zone 14. This maximises the gain of the lens10.

It will be apparent to persons familiar with optical devices that thelens of FIG. 1 has a magnification of 1, for the slats of the lens areall parallel to the lens axis 11. Thus a ray from the source 13 whichmakes an angle α to the lens axis will be reflected once by a slat ofthe lens and the reflected ray will also make an angle α with the lensaxis 11.

FIG. 1 illustrates an ideal construction for a slatted lens with amagnification of 1, with a progressive change in the front-to-backlength, t, of the slats as the distance of the slat from the lens axisincreases. In practice, when many slats are to be incorporated into thelens, the lens construction shown in FIG. 2 will normally be adopted.

The lens shown schematically in FIG. 2 requires slats of three sizesonly. The slats are mounted in groups of identical slats. However, thespacing between the slats of each group is varied progressively so that(as in the lens of FIG. 1) if the angle of incidence of radiation fromthe source 13 on the nth slat from the lens axis is γ_(n) (in practice,because there are many more reflective slats 12 in a practicalrealisation of the lens shown in FIGS. 1 and 2, the angle γ_(n) will notvary significantly over the reflective surface of the nth slat), theratio d_(n) /t_(n) is defined by the relationship: ##EQU7## where d_(n)is the separation (or spacing) between the nth and (n+1)th slats of thelens, and t_(n) is the extent of the nth slat in a direction parallel tothe lens axis 11.

The lens 20 shown in FIG. 3 is another modified form of the lens ofFIG. 1. The main modification in this case is the inclination of theplanar surfaces of the slats 22 relative to the lens axis 21. Forradiation from the source 13, this results in a reduction of the size ofthe focal zone 24, and a consequential increase in the gain and in themagnification of the lens 20. Clearly, if the source of radiation shouldbe located at 24, and the image produced at 13, the lens would have amagnification of less than 1, although it would still have a high gain.

FIG. 4 shows, in FIGS. 4(a) to 4(d), representations of arrays, eachhaving a differently shaped generatrix. The generatrix is defined to bethe line normal to each of the reflectors. Each of FIGS. 4(a) to 4(d)display lenses with plane reflectors or slats. FIG. 4(a) shows an arraywherein the generatrix of the lens is of parabolic shape, to focus aparallel beam, or to produce a collimated beam from a point source. FIG.4(b) shows an array wherein the generatrix of the lens is of ellipticalshape, to focus a converging beam or to produce a diverging beam from apoint source. The generatrix of the lens should be of hyperbolic shapeto focus a diverging beam. It should be convex hyperbolic, as shown inFIG. 4(c) to achieve a high intensity gain in the focal spot, that is,demagnification, and, it should be concave hyperbolic for magnification,as shown in FIG. 4(d). In narrow angle lenses, the generatrix may havethe a parabolic, hyperbolic or elliptic shape, which all approximateclosely to a circle for small off-axis angles.

FIG. 5 illustrates a convenient mechanism for constructing lenses of thetype shown in, FIGS. 1, 3 and 4, when the lenses are to be used withelectromagnetic radiation, such as in the visible spectrum or withultra-violet radiation or infra-red radiation.

The lens of FIG. 5 is constructed of optical quality material which istransparent to the radiation with which the lens is to be used. Thetransparent material must have a refractive index, n, for thatradiation, which is greater than 1.

For radiation in the visible spectrum, a number of plastic materials andglasses can be used in this form of lens construction. Slots 80 are cutinto a block of the transparent material having the required shape ofthe slatted lens to be produced. The slots 80 are made at the locationsof the slats of the required slatted lens. The slot face which isclosest to the axis of the lens must be polished to ensure good lensperformance, and for some applications, each face of the slots should bepolished (this means that for a lens which is equivalent to a lenshaving planar slats, the slot faces will be optically flat). The slots80 need not extend completely through the block of plastic. The frontfaces 85 and the rear faces 86 of the transparent material between theslots must be optically flat faces for good lens performance.

FIG. 5 includes several ray paths from a point source 13 on the lensaxis. It will be noted that each off-axis ray is refracted when itstrikes the front surface 85 of the optical quality transparentmaterial, and then is reflected (by total internal reflection) from theface of the relevant slot 80, before being refracted again at face 86 onleaving the transparent material of the lens.

It will be appreciated that slatted lenses, forming arrays of othershapes (such as the lenses shown in FIG. 4) may be constructed in thismanner, or, by assembling a series of blocks of the optical qualitytransparent material having (i) a refractive index greater than 1 and(ii) polished surfaces having the required slat shape. Each of theassembled blocks will be spaced from its adjacent block or blocks by asmall distance.

FIG. 6 illustrates a lens to focus X-rays similar to that in FIG. 3, butwherein the reflectors are crystals or multi-layer mirrors, andreflection is Bragg reflection.

Various practical applications for the present invention are envisagedby the inventor, as will be described hereafter.

(i) UV, VUV and X-Ray lenses and collimators with high efficiency.

It has been shown that the collection efficiencies of square-channeloptics can be increased by modifying the lens structure. Suchmodifications involve segmenting the plate, or varying channel width, orlocally varying the lens thickness.

FIG. 7 is an illustrative example of a 90° crossed-slats lens 60 whichis constructed using two lenses of the type shown in FIG. 3, the twolenses having a common centre of curvature. Such a 90° crossed-slatslens 60 acts to focus incident radiation from a point source to a focalzone. FIG. 7(a) shows an elevational view in the y-z plane, FIG. 7(b)shows a top view (x-y plane), FIG. 7(c) shows an elevational view in thex-z plane, and FIG. 7(d) illustrates a three dimensional representationof the lens.

A focusing efficiency approaching 100% can be achieved for such a lenswith each channel length t_(n) and channel width d_(n), varying as:##EQU8## where γ_(n) is the angle between the n-th reflector and the rayentering the n-th channel.

The focus will be square with a width M+1 times the maximum channelwidth d_(n). Therefore to achieve tight focusing and high intensity gainit is worthwhile to vary t_(n) to satisfy the above condition. 100%efficiency is achieved only for one particular set of source and imagedistances.

(ii) A UV, VUV and X-ray Beam Homogeniser.

FIG. 8 shows an example of a double array lens designed as a UV, VUV andX-ray beam profile homogeniser to arrange a Gaussian beam into a `tophat` beam, fir material processing. The requirements are that thesurface of the material should be illuminated as uniformly as possibleor shaped for intensity according to particular production requirements.An array of optical devices with the ability to manipulate a beam shapehas a unique potential to develop a low-cost beam homogeniser withminimal power loss. One of the possible schemes to convert a collimatedbeam with Gaussian profile in intensity distribution into a focusingbeam with homogeneous intensity in a particular sample plane is shown inFIG. 8. The first lens is a beam expander (convex parabolic, if the beamis collimated, or hyperbolic in case of diverging beam) and the secondis a focusing lens (hyperbolic). To design such a beam homogeniser, itis necessary to take into account the initial beam divergence,near-field distribution, diffraction effects on reflector edges, and theactual beam size to develop the required intensity distribution over thesample.

(iii) Sky light enhancer made of an array of reflectors.

FIG. 9 shows, in FIGS. 9(a) and 9(b), elevational cross-sectional andtop views, respectively of a practical application of the arrays of thepresent invention embodied as a two dimensional sky-light enhancer madeof blocks of transparent material, formed of plastics or other material,with slots as reflectors for total internal reflection. A similarconfiguration could be constructed utilising `normal` reflectors.

(iv) Elliptical and Hyperbolic array of reflectors for Solarconcentrators

FIG. 10 shows a cross-sectional view of a trough-like solarconcentrator, being another practical application of the presentinvention. The solar concentrator may be made as an array of reflectorswith parabolic, hyperbolic or elliptical shape.

(v) Compound hyperbolic concentrators

FIG. 11(a) represents an example of an array design as a compoundparabolic concentrator. It consists of the right and the left halveswhich belong to different parabolas, where each parabola focuses theradiation as a parallel beam to the axes of each parabola axis intofocal points, both on the absorber. The goal of this design is tomaximise the concentration of radiation coming from different angles.The solution is to increase the slope of the axis of the parabolic curveso that extreme rays within the acceptance angle illuminate the absorberwithin the prescribed dimensions.

FIG. 11(b) represents an example of an array design as a compoundhyperbolic concentrator. It consists of the right and the left halveswhich belong to different hyperbolas, where each hyperbola focuses theradiation coming within the acceptance angle into a focal point. Thegoal of this design is to maximise the concentration of radiation comingwithin the aperture of the concentrator. The solution is to increase thedistance between the axis of the hyperbolic curves so that extremeparallel rays illuminated the absorber within the prescribed dimensions.

It is emphasised that the embodiments of the present invention which areillustrated in the accompanying drawings and described above are onlyexamples of the present invention. Variations of and modifications tothe illustrated lenses may be made without departing from the presentinventive concept.

I claim:
 1. A lens, suitable for directing radiation, comprising anarray of planar reflecting elements, wherein each of said elements areof non-uniform extent or surface area and/or are non-uniformly spacedfrom adjacent elements, and wherein the ratio of d_(n) /t_(n) isdetermined by angle of incidence γ_(n) of radiation on each element ofsaid lens as is given by the relationship: ##EQU9## where d_(n) is thespacing between the nth and (n+1)th adjacent elements of the lens, andt_(n) is the length of the nth element.
 2. A lens as claimed in claim 1,wherein the ratio of d_(n) /t_(n) is determined by angle of incidenceγ_(n) of radiation on each element of said lens as is given by therelationship: ##EQU10## where d_(n) is the spacing between the nth and(n+1)th adjacent elements of the lens, t_(n) is the length of the nthelement, and M is the magnification of the lens.
 3. A lens as claimed inclaim 1, wherein the extent of each of said elements decreases orremains the same relative to adjacent elements, as the distance of eachof said elements from an axis of said lens increases.
 4. A lens asclaimed in claim 1, wherein the spacing between adjacent elementsincreases as the distance of each element from the axis of said lensincreases, whilst the extent of each element remains the same.
 5. A lensas claimed in claim 1, wherein the elements are designed and positionedto minimize shadowing on other elements.
 6. A lens as claimed in claim1, wherein either one or both faces of each of said elements is providedwith a reflective surface.
 7. A lens as claimed in claim 1, wherein thegeneratrix of the lens is of simple or compound, hyperbolic, parabolic,elliptical or circular shape.
 8. A cross-slatted lens, formed of twolenses as claimed in claim 1, wherein their respective elements areplaced with their edges closely adjacent to each other and with theirelements crossed at 90°.
 9. A lens as claimed in claim 1, wherein saidreflective elements are formed as planar slots in transparent materialand whereby reflection is due to total internal reflection.
 10. A lensas claimed in claim 1, wherein said reflective elements are crystals ormulti-layer mirrors and reflection is due to Bragg reflection.
 11. Adouble array lens comprised of two lenses as claimed in claim 1, whereinsaid double array lens is used as a beam profile homogenizer to arrangea first type of beam into a second type of beam.
 12. A lens as claimedin claim 1, wherein said lens is utilized as a sky-light enhancer.
 13. Alens as claimed in claim 1, wherein said lens is utilized as a solarconcentrator.
 14. A cross-slatted lens formed of two lenses as claimedin claim 1, wherein their respective elements are placed with theiredges abutting each other and with their elements crossed at 90°.